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Based on the $t-t'-U-V$ model with proper chosen parameters for describingthe cuprate superconductors, it is found that near the optimal doping at lowtemperature ($T$), only the pure d-wave superconductivity ($d$SC) prevails andthe antiferromagnetic (AF) order is completely suppressed. At higher $T$, theAF order with stripe modulation and the accompanying charge order may emerge,and they could exist above the $d$SC transition temperature. We calculate thelocal differential tunnelling conductance (LDTC) from the local density ofstates (LDOS) and show that their energy variations are rather different fromeach other as $T$ increases. Although the calculated modulation periodicity inthe LDTC/LDOS and bias energy dependence of the Fourier amplitude of LDTC inthe "pseudogap" region are in good agreement with the recent STM experiment[Vershinin $et al.$, Science {\bf 303}, 1995 (2004)], we point out that some ofthe energy dependent features in the LDTC do not represent the intrinsiccharacteristics of the sample

Temperature dependence of the local tunneling conductance in cuprate superconductors with competing antiferromagnetic order